Reflection groups in algebraic geometry

By Igor Dolgachev. 2006

87 citations recorded by the source corpus.

After a brief exposition of the theory of discrete reflection groups in spherical, euclidean and hyperbolic geometry as well as their analogs in complex spaces, we present a survey of appearances of these groups in various areas of algebraic geometry.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0da8893b2572d5ca17642fe201d78db39428bad4

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

A brief introduction to Enriques surfaces (2014, background): “the subgroup Ref2(E2,4,6) generated by reflections in vectors α with α(2) = −2 is of finite index in the orthogonal group (see [27], Example 4.”
Classical Algebraic Geometry: A Modern View (2012, background): “It follows from the theory of groups generated by reflections (see, for example, [188], 4.”
Rational surfaces with a large group of automorphisms (2011, background): “It is known that the groupWX does not depend on a choice of a geometric basis (see [17], Theorem 5.”
Normal subgroups in the Cremona group (2010, background): “A proof is sketched in [24, 23], and a complete, characteristic free, proof is available in [7]; analogous result and proof for generic Enriques surfaces can be found in [21].”